Relaxation Dynamics of Semiflexible Fractal Macromolecules

Abstract

Abstract:We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

“…Step-like structures have also been observed for different quantities depending only on the spectrum, such as the storage and loss moduli for fractal polymers [22].…”

Marginally compact fractal trees with semiflexibility

“…4 we exemplify the spectra for T 1 and T 2 having stiffness parameter q = 0 (fully-flexible case) and q = 0.9 (semiflexible case). As it is typical for semiflexible trees [40][41][42][43]51], switching on the stiffness leads to an increase of higher eigenvalues (due to the restricted local vibrations) and a decrease of the lower ones (due to the growth of the trees' size). Here, the lower eigenvalues scale with the mode number p as λ p ∼ p 5/3 , notwithstanding their non-smooth behavior reflecting the degeneracy of eigenvalues.…”

“…The symmetry of trees T 1 and T 2 allows an iterative construction of a full set of eigenvectors [49]. The construction procedure is rooted in the work of Cai and Chen [50] for flexible dendrimers, which has been extended to STP treatment of semiflexible dendrimers [40,41] and regular fractals [42,43].…”

“…Notwithstanding this difficulty, the framework of semiflexible treelike polymers (STP) of Ref. [39], where the semiflexibility is introduced at all beads (also at branching nodes), turned out to be very helpful in studying the relaxation dynamics of semiflexible dendrimers [40,41] and fractals [42,43]. Moreover, inclusion of bond-bond correlations has been shown to have a fundamental importance for NMR relaxation of dendrimers [44][45][46][47].…”